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Your last sample can be written as
#!/bin/bash
LOG_DIRS="/Sandbox/logs1 /Sandbox/logs2 /Sandbox/logs3 /Sandbox/logs4"
for log_dir in $LOG_DIRS
do
for file in "$log_dir"/*
do
# ensure...

You don't need an array here.
LOG_FILES="/Sandbox/logs1/* /Sandbox/logs2/* /Sandbox/logs3/* /Sandbox/logs4/*"
for file in $LOG_FILES
do
...

Or go for one more loop....